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Galaxy Population Identification With

a Phylogenetic Approach

Por: MONSERRAT LORETO MARTINEZ MARIN

Tesis presentada a la Facultad de Ciencias Físicas y Matemáticas de la

Univerisdad de Concepción para optar al grado académico de Magíster en

Astronomía.

Profesor Guía: Dr. Ricardo Demarco López

Comisión: Dr. Ricardo Demarco López, Dr. Guillermo Cabrera

Vives & Dr. Neil Nagar

Enero 2020

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© 2019, Monserrat Loreto Martínez Marín

Ninguna parte de esta tesis puede reproducirse o transmitirse bajo ninguna forma o por ningún medio o procedimiento, sin permiso por escrito del autor.

Se autoriza la reproducción total o parcial, con fines académicos, por cualquier medio o procedimiento, incluyendo la cita bibliográfica del documento

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Acknowledgement

I would first like to thank my thesis advisor Ricado Demarco, for his advice, encouragement and trust placed in me to do this job. As well as my co-advisor Guillermo Cabrera for his extraordinary support and always steered me in the right direction whenever I needed it. I would also like to thank the experts who were involved in this work, Dr. Pierluigi Cerulo, Dr. Rodrigo Herrera, Dr. Nathan Leigh and Dr. Inger Jørgensen. Without their passionate participation, valuable comments and advises, this thesis could not have been successfully conducted.

I wish to acknowledge the support and great love of my family, my mother, Loreto; For his unconditional love even when I’m the biggest scare of his life, my father, Osvaldo; For instilling curiosity in science from an early age. My brother and sister, Nelson and Micaela; For their care and love, my friends Mariela, Catalina, Paulo, Carolina, Daniela and Ignacio; For being my second family. And finally my significant other, Paula; Because without her love none of this would be possible.

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ii

Summary

Galaxy evolution is one of the main open questions in modern astrophysics. Theories of evolution arise from the observed morphological differences of galaxies. We propose a new approach interpreting the results without previously biasing the sample by a specific characteristic of galaxies like mass, morphology, sSFR or metallicity. For this we make a phylogenetic analysis at different environments like Coma cluster to 475 galaxies with redshifts0,015< z <0,033and 438 galaxies of the coeval field with redshifts

0,035< z <0,054. The phylogenetic study retrieve possible evolutionary paths for galaxies

based on the information of stellar population of galaxies by a set of 30 absorption indices from the Sloan Digital Sky Survey (SDSS). The branches of the tree are interpreted as galaxy populations and the length between the nodes (NodeLength) as the internal chemical variation of the galaxy population. The NodeLength works as chemical index, thus connecting galaxy stellar populations with other structural and local environmental properties of galaxies. We found a contrast of how galaxies are chemically related at different environments, the Coma cluster is a complex systems with multiple populations of galaxies, while the field is a more homogeneous population, presenting one main galaxy population. The Coma cluster present three main galaxy populations and several minor structures in the Red Sequence of the Color-Magnitude Diagram. The main populations we find in Coma are 3: (i) One mostly of S0 morphology, which internal hierarchical structure shows correlations with stellar age, metallicity, and sSFR, NaD index. This tells us that galaxies of this population has suffered a recent period of star formation;(ii) another one with mostly elliptical morphology, do not show internal correlations and has old quenched galaxies with high metallicity and stellar mass; and (iii) one that has the youngest galaxies with spiral and lenticular morphology, which belong to the blue cloud of the Cluster. This population do not show internal correlations, but their galaxies with S0 morphology, show a chemical correlation with F e4383 not present in other galaxy populations with the same morphology. On the other hand the main population present in the field, has an internal hierarchical structure that show a weak correlation with sSFR, but not dependence with any specific absorption index.

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Abstract

We propose a phylogenetic approach as a novel and robust tool capable of detecting galaxy populations (GPs) based on their chemical composition. This method clusters galaxies into the hierarchical structure of a phylogenetic tree that connects galaxies through features we call "nodes". The branches of the tree are interpreted as different GPs and the length between nodes (NodeLength) as the internal chemical variation along a branch. The NodeLength works as a chemical index, thus relating galaxy stellar populations with other structural and local environmental properties of galaxies. We apply the phylogenetic approach using 30 abundance indices from the Sloan Digital Sky Survey to 475 galaxies in the Coma cluster (0,015< z <0,033) and 438 galaxies in the field (0,035< z < 0,054). We find that Coma is a complex system with multiple populations. It has three main GPs that can readily be identified in color-magnitude space, and several minor structures in its red sequence. On the other hand, the field is more homogeneous, presenting one main GP. This phylogenetic analysis of cluster and field galaxies, shows a contrast in terms of how chemically related galaxies are within different environments. We also find that, regardless of their morphology, galaxies can have a similar chemical composition. Therefore, this new approach to study galaxy properties and their evolution makes it possible to perform robust analyses and interpretations without introducing biases by first selecting samples based on a specific characteristic like stellar mass, morphology, sSFR or metallicity, as done with more traditional techniques.

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iv Table of Contents

Table of Contents

Acknowledgement i

Summary ii

Abstract iii

1. Introduction 1

1.1. Cladistics for astrophysics . . . 1

1.2. Phylogenetics based on DM . . . 1

1.3. Galaxy evolution . . . 2

2. Theoretical Framework 5 2.1. Research Problem . . . 5

2.2. Research Question . . . 5

2.3. Problem Statement . . . 5

2.4. Hypotesis . . . 6

3. Data 7 3.1. Phylogenetic study for Globular Cluster . . . 7

3.2. Phylogenetic study for Galaxies . . . 7

3.2.1. Phylogenetic Study . . . 7

3.2.2. Comparison data . . . 7

4. Methodology 9 4.1. Phylogenetic Tree . . . 9

5. Analysis 21 5.1. Proof of concept . . . 21

5.1.1. Globular Cluster NGC2808 . . . 21

5.2. Phylogenetic study in Galaxies . . . 25

5.2.1. The Coma Cluster . . . 25

5.2.2. The Field . . . 36

6. Discussion 47 6.1. Comparison with other methods . . . 47

6.2. Minor Structures . . . 49

7. Conclusion 52

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5.1. Galaxy distribution in the Phylogenetic tree of the Coma Cluster . . . . 25 5.2. Pearson and Spearman coefficients between NodeLength and common

properties of galaxies for each galaxy population . . . 34 5.3. Remaining galaxy populations for Recalculated phylogenetic trees without

a specific set of line indices . . . 36 5.4. Pearson and Spearman coefficients between NodeLength and common

properties of galaxies for each galaxy population . . . 41 5.5. Pearson and Spearman coefficients between NodeLength and specific

abundance indices for each galaxy population in the field . . . 46 6.1. Pearson and Spearman coefficients between NodeLength and common

properties of galaxies for each galaxy population . . . 50 6.2. Pearson and Spearman coefficients between NodeLength and specific

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vi List of Figures

List of Figures

4.1. Star representation distribution of galaxies of our example, the branches in black represent the unknown length. . . 10 4.2. Star representation of the distribution of our galaxy sample in our first

cycle, the branches in black represent the unknown length and red branches represent Know distances. . . 12 4.3. Star representation of the distribution of our galaxy sample in the second

cycle. The branches in black represent the unknown length and red branches represent Know distances. In this cycle we have two nodes represented by letter U, that joins different galaxies. . . 15 4.4. Star representation of the distribution of our galaxy sample in our third

cycle. The branches in black represent the unknown length and red branches represent Know distances. We have a tree with three nodes represented by letter U. . . 17 4.5. Star representation of the distribution of our galaxy sample in our four

cycle, the branches in black represent the unknown length and red branches represent Know distances. . . 18 4.6. Final Star representation of the distribution of our galaxy sample, the

branches in black represent the unknown length and red branches represent Know distances. The U letters represent the nodes between galaxies. . . . 19 4.7. Final Phylogenetic tree, each galaxy is represented by a letter at the end

of the branches. Each branch is joined to an specific node U. The numbers represent the length of the branches. . . 19 5.1. Consensus phylogenetic tree of the globular cluster NGC2808. The red

shaded area highlight the main branch of the phylogenetic tree. The numbers correspond to the ID of each star in the globular cluster. . . 22 5.2. Mg and Na anticorrelation from figure 8 C15. Different colours indicate

different groups, blue (P1), green (P2), red (I1), orange (I2), and black (E) 23 5.3. Na-Mg anticorrelation of the globular cluster NGC2808, with the five groups

define by C15 differentiated by color. Blue (P1), green (P2), red (I1), orange (I2), and black (E). The magenta hollow squares represent the stars in our

main branch of the phylogenetic tree. . . 24 5.4. Color-Magnitude diagram of the Coma Cluster with photometric filters

Johnson B and Sloan r. Triangles, circles and squares represent galaxies belonging to branch 1 (B1), branch 2 (B2) and branch 3 (B3), respectively. The colors indicate galaxy morphology where red corresponds to elliptical galaxies, blue to spiral galaxies, and yellow to S0 galaxies. . . 26 5.5. Branch B1 of the phylogenetic tree of the Coma Cluster that represents

our first galaxy population. Each galaxy has its ID number from the SDSS DR7, and its image from the SkyServer DR15. The number between the nodes is the length of their separation. . . 27 5.6. Branch B2 of the phylogenetic tree of the Coma Cluster that represents

our second galaxy population. Each galaxy has its ID number from the SDSS DR7, and its image from the SkyServer DR15. The number between the nodes is the chemical length of their separation. . . 28

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third galaxy population. Each galaxy has its ID number from the SDSS DR7, and its image from the SkyServer DR15. The number between the nodes is the length of their separation. . . 29 5.8. Projected sky distribution of galaxies in the Coma Cluster belonging to

different branches of the phylogenetic tree. Triangles, circles and squares represent galaxies belonging to branch 1 (B1), branch 2 (B2) and branch 3 (B3), respectively. The colors indicate the morphology of the galaxy where red corresponds to elliptical galaxies, black to spiral galaxies, and magenta to S0 galaxies. The color scale shows the number count of galaxies by degree squared in the sky for Coma cluster. White star points the galaxy NGC4839. 31 5.9. The histograms A, B, C and D show the distribution of galaxies from

the three different branches B1, B2 and B3 with respect to stellar mass, metallicity, age and sSFR. The yellow, red and blue colors represent galaxies from branches B1, B2 and B3, respectively. . . 32 5.10. Panels A, B, C and D, show a comparison of our chemical index (length

between nodes) with stellar mass, metalicity, age of the stellar population, and sSFR, respectively. Triangles, circles and squares represent B1, B2 and B3 GP. The red, yellow and blue colors represent elliptical, lenticular and spiral morphology, respectively. . . 33 5.11. Color-magnitude diagram of our Coma cluster galaxy sample with

photometric filters Johnson B and Sloan r. Panels A, B, C, D, and E show a recalculated phylogenetic tree without, negative response toα/F e

enhancement, insensitive response to α/F eenhancement, positive response

toα/F e enhancement, absorption Balmer lines, and absorption line indices

[OIII], respectively. The cyan diamonds represent the galaxies that appear in the branches of each recalculated tree. . . 37 5.12. . . 38 5.13. Continue image . . . 39 5.14. Comparison of absorption lines with length between nodes of our GP.

Triangles, circles and squares represent the B1, B2, and B3 GP. The red, yellow and blue colors represent elliptical, lenticular and spiral morphology, respectively. Red, yellow and blue lines correspond to linear fits to each galaxy population. The Spearman correlation (SC) index is calculated for each galaxy population. . . 40 5.15. Spatial distribution of our field galaxy sample in the sky. Grey circles

represent all galaxies in our sample, whereas triangles represent our main galaxy population. Red, yellow, and blue colors indicates, correspondingly, elliptical, S0 and spiral galaxies. . . 42 5.16. Galaxy population obtained in the field, plotted as a single tree. Each

galaxy has its ID number from the SDSS DR7, and its image is from the SkyServer DR15. . . 43 5.17. Panels A, B, C, and D show a comparison of our chemical index (length

between nodes) with stellar mass, metallicity, age of the stellar population and sSFR, respectively. Red, yellow and blue colors represent the elliptical, S0 or spiral morphology, respectively, of our galaxy population in the field. 44

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viii List of Figures

5.18. Color-magnitude diagram of our field galaxy sample, where panels A, B, C, D, and E show a recalculated phylogenetic tree excluding absorption Balmer lines, lines insensitive to α/F e, lines with negative response to

α/F e enhancement, lines with positive response to α/F e enhancement,

and Emission Line [OIII]α5007, with [OIII1] and [OIII2] respectively.

The cyan diamonds represent the galaxies that appear in branches of each recalculated tree. . . 45 6.1. Principal component decomposition of the 30 abundance indices for our

galaxy samples of the Coma cluster and the field. Figure A present the principal components 1 and 2, and B present the principal components 1 and 4 for the Coma cluster. Figure C present the principal components 1 and 2, and D present the principal components 1 and 4 for the field. Red, blue and yellow dots, indicates the elliptical, spiral and lenticular morphology of the galaxies. Magenta and cyan diamonds indicates the centroids for the PCA decomposition . . . 48 6.2. Minor structures. Image A show a Color-Magnitude diagram of the Coma

Cluster with photometric filters Johnson B and Sloan r, image B show a PCA decomposition of the coma cluster and image C show a PCA decomposition of the field. Triangles, circles and squares represent galaxies belonging to branch 1 (B1), branch 2 (B2) and branch 3 (B3), respectively. The colors indicate galaxy morphology where red corresponds to elliptical galaxies, blue to spiral galaxies, and yellow to S0 galaxies. Black and grey dots indicates the structures with 1, 2 and 3 nodes and single branch respectively. . . 51

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1.

Introduction

In the last years, phyloinformatic studies have been used in astronomy to help understand different processes that could involve evolution. These studies were based either on discrete character states (DC) or distance matrices of pairwise dissimilarities (Dm). Their main objective is to study the evolutionary history and relationships among individual or groups of astronomical objects.

1.1.

Cladistics for astrophysics

Astrocladistics is a Maximum parsimony method, that can be utilize as a tool to find hierarchical classification of galaxies. This classification is based on choosing specific characters to compare states of evolution. The characters can be either qualitative (e.g. morphology) or quantitative (e.g. luminosity, stellar mass, chemical composition). In order to compare this characters two states have to be defined, one have to be ancestral and the other one derived. This hierarchical classification is represented in a phylogenetic tree, called a cladogram, in which the distance between two branches reflects the level of diversification that occurred during evolution. Astrocladistics essentially attempts to represent the pattern of morphological similarity. Some examples applied to astronomy of astrocladistics are the morphological relation in dwarf galaxies of the Local Group (Fraix-Burnet et al. 2006), globular cluster classification (Fraix-Burnet et al. 2009) and

stellar populations (SP) in ω Centauri (Fraix-Burnet and Davoust 2015).

1.2.

Phylogenetics based on DM

Other method for inferring phylogenetic trees is based on a distance-matrix. Here we calculate some measure of dissimilarity that for our case study are absorption lines indices of each pair of galaxies, to produce a pairwise distance matrix, and then infer with the neighbour joining algorithm the phylogenetic relationships of the galaxies from that matrix. The neighbour joining algorithm constructs a tree by sequentially finding pairs of neighbours, which in our study are pairs of galaxies connected by a single interior

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2 1.3 Galaxy evolution

node. The main difference of NJ from other clustering algorithms is that it minimizes the length of all internal branches and thus the length of the entire tree. This way we can represent the branching pattern of evolution. This method was employed as an attempt to reconstruct the chemical history of stars in the solar neighbourhood (Jofré et al. 2017) and to retrieve stars from an open cluster (Blanco-Cuaresma and Fraix-Burnet 2018).

1.3.

Galaxy evolution

The utility of phylogenetics studies in galaxies, came from the necessity of find a reliable method to solve galaxy evolution which remains as an open problem in modern astrophysics. Galaxies are complex systems made up of stars, gas, dust and dark matter. Galaxy evolution is the result of several complex physical processes that involve the various galaxy components in different ways through cosmic epochs. These mechanisms bring galaxies to transition from one physical state to another and to change their observed properties. Morphology is the most immediate way to classify galaxies since it is based on a visual assessment. Following Hubble (Hubble, 1926), galaxies are classified as ellipticals, lenticulars or S0s, and spirals. A class of irregular galaxies is added to take into account objects that cannot be classified neither as elliptical, S0 or spiral. Ellipticals and S0s are commonly said early-type galaxies (ETGs), while spirals and irregulars are commonly grouped together as late-type galaxies (LTGs). (although see Scarlata et al. 2007, Huertas-Company et al. 2008, Pérez-Carrasco et al. 2019 for examples of automated, machine-learning-based morphological classification). Morphology is related to the underlying structural distribution of the stellar populations and interstellar medium. ETGs tend to be red and with no or little star-formation, while LTGs tend to be blue and star-forming (see Baldry et al. 2004, Cassata et al. 2008, Taylor et al. 2015). Up to z ∼ 6, the star formation in galaxies is observed to be related to their stellar mass: massive galaxies are less star-forming than their low-mass counterparts (Cowie et al., 1996). The stellar mass of galaxies is finally related to their metallicity: more massive galaxies are also metal-richer (Lequeux et al. 1979; Tremonti et al. 2004; Gallazzi et al. 2005)

Regardless of the environment where galaxies reside, they show a bimodal colour distribution. Three main populations can be defined from this color-magnitude distribution:

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and (3) a diffuse cloud of blue star-forming galaxies. Thus, in principle, the evolution of a galaxy population can be investigated by looking at the gradual build-up of the Red Sequence as a function of redshift (Tanaka et al. 2010; Gobat et al. 2011;Muzzin et al. 2012; Lidman et al. 2004; Snyder et al. 2012).

Nevertheless, we can obtain more detailed information by studying galaxy spectra. Spectra of galaxies have information about gas and stellar populations properties that preserved record of galaxy’s formation and evolution. Emission lines are used to study the physical state of the ionized gas, so we can trace black hole accretion, derive gas kinematics and star formation activity (Kauffmann et al. 2003; Schawinski et al. 2007). Absorption lines provides information of stellar populations properties and can be used to derive ages, metallicities, star formation histories and element abundances.(Davies et al. 1993; Fisher et al. 1996; Jørgensen 1999; Kuntschner 2000; Thomas et al. 2010a). The most common sets of optical absorption line indices are the Lick index system (Burstein et al. 1984; Faber et al. 1985; Worthey 1994; Worthey and Ottaviani 1997), and the [OIII] indices ( González 1993). This indices group different absorption lines, therefore they measure various chemical elements, and the derivation of the abundance for an individual element abundances is non-trivial.

Studies with absorption lines compare morphology with chemical abundances and other properties like velocity dispersion (Davies et al. 1987, Burstein et al. 1988), B-band absolute magnitudes ( Faber 1973; Terlevich and Melnick 1981), or effective radius (Parikh et al. 2018).

In this work we propose a new perspective to study galaxy evolution, by analyzing the grouping of galaxies according to their chemical composition through a phylogenetic approach utilizing multiple absorption indices. For this, we analyzed the stellar population chemical information of galaxies in different environments. We considered 475 galaxies in the Coma cluster of galaxies with redshifts 0,015< z <0,033, and 438 field galaxies with redshifts 0,035 < z <0,054. Utilizing a set of 30 lines indices from the value added catalogs of the Sloan Digital Sky Survey data release 14 (SDSS) (Abolfathi et al. 2018). We generated a phylogenetic tree based on a distance matrix from the pairwise differences of these indices with the Neighbor Joining algorithm (NJ; Saitou and Nei 1987; Studier

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4 1.3 Galaxy evolution

and Keppler 1988). NJ allows us to find hierarchical relationships that can be used to uncover possible evolutionary paths of the observed galaxies. We interpret the branches of the phylogenetic tree as different galaxy populations, and the length between nodes of this branches as a gradient of chemical difference in the stellar population content of these galaxies. In this way we analyze galaxy evolution avoiding linearity, to see then how properties like morphology, stellar mass (M∗), star formation rate (SF R), specific star

formation rate (sSFR; SF R/M∗) or metallicity ([Z/H]) relate with galaxy populations in

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2.

Theoretical Framework

2.1.

Research Problem

In modern astronomy, physical relationships that link galaxy populations with galaxy evolution are not well defined yet with enough amount of detail. Since Hubble introduced his classification of galaxies based on morphology, astronomers have wondered whether this implies that galaxies evolve. Therefore, they have studied possible internal and external physical processes that could be responsible for this evolution. However, the selection criteria for galaxy populations are biased by morphology or other properties like (stellar or dynamical) mass, star formation rate, metallicity and age.

2.2.

Research Question

Can we utilize a Phylogenetic tree as a method to identify galaxy populations and obtain a useful physical insight to study galaxy evolution?

2.3.

Problem Statement

In the last years, phylogenetic trees have been used in astronomy to study processes that involve evolution. They are based on the chemical content of astronomical objects, and are able to disentangle them into different populations represented as the branches of the tree. The aim of this work is the utilization of this method on galaxies to identify different populations by using a set of absorption line indices. In order to have a physical insight about their chemical composition, we define an index given by the length between the so-called nodes of the branches that reflect a chemical gradient between galaxies within a population. This allows us to visualize which absorption lines are prominent, aiming at being able to better characterize and describe the overall star formation history of galaxies.

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6 2.4 Hypotesis

2.4.

Hypotesis

Phylogenetic trees can be used to identify galaxy populations and give us a physical insight about them to study galaxy evolution.

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3.

Data

3.1.

Phylogenetic study for Globular Cluster

For the globular cluster NGC2808 we use the membership of stars from ?, obtaining 117 stars with 11 chemical abundances of [O/F e]I,[N a/F e]I,[M g/F e]I ,[Si/F e]I,[Ca/F e]I,

[Sc/F e]II, [T i/F e]I, [Cr/F e]I, [F e/H]I, [F e/H]II,[N i/F e]I, with they corresponding

errors.

3.2.

Phylogenetic study for Galaxies

3.2.1.

Phylogenetic Study

For the phylogentic study on the Coma cluster we use the membership of Beijersbergen et al. 2002, obtaining 475 galaxies with redshifts from 0,015 to 0,033. For the field we selected galaxies that do not belong to galaxy groups (Tempel et al. 2012) nor filaments (Tempel et al. 2014), thus obtaining a sample of 438 galaxies with redshifts from 0,035 to 0,054. For both samples we obtained the spectroscopic data from the seventh data release (DR7 Abazajian et al. 2009) of the Sloan Digital Sky Survey (SDSS;York et al. 2000 ). We used the spectral line strength measurement database provided by the OSSY group (Oh et al. 2011), considering the stellar absorption-line measurements for this galaxy sample.

3.2.2.

Comparison data

The stellar mass is based on fits to the photometry following (Kauffmann et al. 2003), and (Salim et al. 2007) from the SDSS DR7. The SF R estimates are based on the technique

discussed in Brinchmann et al. 2004, with a slight modification for non-star-forming galaxies where the likelihood distribution of the sSFR was constructed as a function of D4000 using the star-forming sample, also from the SDSS DR7. The ages and metallicities where calculated following Cardiel et al. 2003 with the Thomas et al. 2010b models. Finally, we utilized the visual morphological classification by TType from van Dokkum

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8 3.2 Phylogenetic study for Galaxies

2001 and two parameters of the morphological classification from Domínguez Sánchez et al. 2018, obtained with deep learning algorithms using convolutional neural networks (CNNs). The TType parameter separates ETGs from LTGs and gives the probabilityPS0

of being S0 versus a pure elliptical in order to have three galaxy classes: Elliptical, Spiral and S0. Elliptical galaxies were define such that have TType values from −3 to 0 and

PS0 lower than 0,5. S0 galaxies have TType values between −1 and 3, and PS0 higher

than 0,5. Finally, Spiral galaxies have a TType value between 3and8, independent of the

PS0 value. For galaxies in the sample that do not have information on TType and PS0, a visual morphological classification was assigned.

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4.

Methodology

4.1.

Phylogenetic Tree

We perform a phylogenetic study based on a distance matrix with the NJ algorithm utilizing the open-source Scikit-bio python package. In our case study, the distance matrix elements are obtained by the summation of the euclidean distance for a given abundance index (Xk) between every pair of galaxies in our sample. Therefore, each element of our

distance matrix is the total chemical distance Di,j from our set of abundance indices between our galaxies:

Di,j =

N

X

k=1

|[Xk]i−[Xk]j|

For example if we have the following distance matrix:

               

GA GB GC GD GE GF

GA 0 5 4 7 6 8

GB 5 0 7 10 9 11

GC 4 7 0 7 6 8

GD 7 10 7 0 5 9

GE 6 9 6 5 0 8

GF 8 11 8 9 8 0

               

.

The molecular clock hypothesis states that the rate of nucleotide substitution per generation is constant across lineages. If generation times were equal across lineages, samples obtained at the same calendar time would have experienced the same number of generations since their common ancestor

A clustering method would group galaxies A and C as the most similar galaxies, because their total chemical distance Di,j is the smallest. This would assume that the elements under study evolve in a clock-like behavior, therefore the samples obtained at the same

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10 4.1 Phylogenetic Tree

calendar time generation time would have experienced the same number of generations since their common ancestor, maintaining a constant rate of change per generation. Nevertheless the main characteristic of NJ is that it takes into account the development of evolution at different rates. For that, the NJ defines a new distance Mi,j∗ which subtracts

the divergence (a summation over the total chemical distance Di,j of each possible pair of galaxies) from the original distance, and normalizes the result by the number of end nodes N:

We will solve step by step an example of six galaxies, utilizing a star representation as we can see in figure 4.7.

Figura 4.1: Star representation distribution of galaxies of our example, the branches in black represent the unknown length.

To know they rate corrected distances we, calculate their divergence with the following equation:

Sj =

P

i≤jDi,j

N −2

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SA =

5 + 4 + 7 + 6 + 8

4−2 = 7,5 SB =

5+7+10+9+11

4−2 = 10,5

SC =

4 + 7 + 7 + 6 + 8

4−2 = 8 SD =

7+10+7+5+9

4−2 = 9,5

SE =

6 + 9 + 6 + 5 + 8

4−2 = 8,5 SF =

8+11+8+9+8

4−2 = 11

With the divergences calculated, we will obtain the new rate corrected distances.

Mi,j∗ =Di,j−(Si+Sj)

This rate corrected distance allow to group the the closest nodes, but at the same time the ones that are further of the rest of the galaxies.

MA,B∗ =DA,B−(SA+SB) = 5−7,5−10,5 =−13

MA,D∗ =−10 MA,E∗ =−10 MA,F∗ =−10,5

MB,C∗ =−11,5 MB,D∗ =−10 MB,E∗ =−11

MB,F∗ =−10,5 MC,D∗ =−10,5 MC,E∗ =−10,5

MC,F∗ =−11 MD,E∗ =−13 MD,F∗ =−11,5

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12 4.1 Phylogenetic Tree

With this new rate corrected distance, we create a new distance matrix.

               

GA GB GC GD GE GF

GA 0 −13 −11,5 −10 −10 −10,5

GB −13 0 −11,5 −10 −11 −10,5

GC −11,5 −11,5 0 −10,5 −10,5 −11

GD −10 −10 −10,5 0 −13 −11,5

GE −10 −11 −10,5 −13 0 −11,5

GF −10,5 −10,5 −11 −11,5 −11,5 0

               

Now we will create our first node U1 with galaxies A and E for whichMi,j∗ is minimal, but we could also choose galaxies D and E. The decision of selecting one or other node will define the the zero point of our tree. We can calculate the length of the branches from each galaxy to this node.

SB,U1 =

D1+SB−SA

N −2 ·

1

2 = 1

SA,U1 =

D1+SA−SE

N −2 ·

1 2 = 4

Figura 4.2: Star representation of the distribution of our galaxy sample in our first cycle, the branches in black represent the unknown length and red branches represent Know distances.

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Now we compute new distances from node U1 to each other terminal node.

dC,U1 =

(dC,A+dC,B −dA,B)

N −2 = 3

dD,U1 =

(dD,A+dD,B−dA,B)

N −2 = 6

dE,U1 =

(dE,A+dE,B−dA,B)

N −2 = 5

dF,U1 =

(dF,A+dF,B−dA,B)

N −2 = 7

We create the new distance matrix.

            

U1 GC GD GE GF

U1 0 3 6 5 7

GC 3 0 7 6 8

GD 6 7 0 5 9

GE 5 6 5 0 8

GF 7 8 9 8 0

            

With this new distance matrix, we start a new cycle to find chemical relationships between our galaxies. Therefore we compute the new divergences for the galaxies that we have left.

N = 5 Number of end-nodes.

SU =

3 + 6 + 5 + 7

5−2 = 7 SC =

3+7+6+8

3 = 8

SD =

6 + 7 + 5 + 9

3 = 9 SE =

5+6+5+8

3 = 8

SF =

7 + 8 + 9 + 8

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14 4.1 Phylogenetic Tree

Now we compute the rate corrected distances

MU,C∗ =−12 MU,D∗ =−10 MU,E∗ =−11

MU,F∗ =−10,6 MC,D∗ =−10 MC,E∗ =−11

MC,F∗ =−10,6 MD,E∗ =−12 MD,F∗ =−10,6

MF,E∗ =−10,6

With this new rate corrected distance, we create a new distance matrix.

            

U1 GC GD GE GF

U1 0 −12 −10 −11 −10,6

GC −12 0 −10 −11 −10,6

GD −10 −10 0 −12 −10,6

GE −11 −11 −12 0 −10,6

GF −10,6 −10,6 −10,6 −10,6 0

            

This new rate corrected distance matrix, show us that the new node could be either galaxies D and E or Node U with galaxy C, we will choose galaxies D and E to have the nodeU2.

SD,U2 = 3

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Figura 4.3: Star representation of the distribution of our galaxy sample in the second cycle. The branches in black represent the unknown length and red branches represent Know distances. In this cycle we have two nodes represented by letter U, that joins different galaxies.

We calculate the new distances to each galaxy.

N = 4 Number of end-nodes.

dU2,U1 =

(dD,U1 +dD,U1 −dD,E)

N −2 = 3

dC,U1 = 3

dF,U1 = 7

The distances between nodes like dU2,U1 will be use later as a chemical index that will

show a chemical gradient useful to differentiate galaxies.

         

U1 GC U2 GF

U1 0 3 3 7

GC 3 0 4 8

U2 3 4 0 6

GF 7 8 6 0

         

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16 4.1 Phylogenetic Tree

We start the third cycle of computation, we already have to nodes in our tree and we need to complete our tree calculating the new divergences for the galaxies that we have left.

SU1 =

3 + 3 + 7

4−2 = 6,5 SC =

3+4+8

2 = 7,5

SU2 =

3 + 4 + 6

2 = 6,5 SF =

7+8+6

2 = 10,5

Now we compute the rate corrected distances

MU

1,C =−11 M

U1,U2 =−10 M

U1,F =−10

MC,U

2 =−10 M

C,F =−10 M

U2,F =−10

With this new rate corrected distance, we create a new distance matrix

         

U1 GC U2 GF

U1 0 −11 −10 −10

GC −11 0 −10 −10

U2 −10 −10 0 −10

GF −10 −10 −10 0

         

The new node joins galaxies C and node U1, and we name it U3.

SC,UU1,C = 2

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Figura 4.4: Star representation of the distribution of our galaxy sample in our third cycle. The branches in black represent the unknown length and red branches represent Know distances. We have a tree with three nodes represented by letter U.

We calculate the new distances to make our forth and final cycle to finish our tree.N = 3 Number of endnodes.

SU2,U3 =

(SC,A+SC,B −SA,B)

N −2 = 3

SU2,F = 6

SU3,F = 6

      

U2 U3 GF

U2 0 3 6

U3 3 0 6

GF 6 6 0

      

SU2 =

2 + 6

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18 4.1 Phylogenetic Tree

MU2,F = 6˘8˘12 = ˘14 MU3,F = 6˘8˘12 = ˘14 MU2,U3 = 2˘8˘8 = ˘14

Here we could choose the combinations U4 =U2,F, U4 =U3,F or U4 =UU2,U3 for our final

node.

SU2,U4 = 1

SU3,U4 = 1

Now we finalize our tree joining F with U4 with branch length 5.

Figura 4.5: Star representation of the distribution of our galaxy sample in our four cycle, the branches in black represent the unknown length and red branches represent Know distances.

We can no longer keep on calculating distances, and we only have left the galaxy F, therefore we calculate it distance to the last node.

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Figura 4.6: Final Star representation of the distribution of our galaxy sample, the branches in black represent the unknown length and red branches represent Know distances. The U letters represent the nodes between galaxies.

Now we have the distances for all our galaxies and we can form our final tree.

C

B

A

E

D F 4

1 1

2

3 5 1 1

1

U1

U2 U3

U4

Figura 4.7: Final Phylogenetic tree, each galaxy is represented by a letter at the end of the branches. Each branch is joined to an specific node U. The numbers represent the length of the branches.

With this algorithm galaxies that have similar chemical composition, galaxies A and B, belong to the same node at the top of the tree. Their next closest neighbour in stellar content is galaxy C. Galaxies A, B and C belong to the same branch which we interpret

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20 4.1 Phylogenetic Tree

as the same GP. In contrast, galaxies E and D belong to another branch separated by node U4, therefore, a different GP. On the other hand, galaxy F does not belong to any

GP. The distance between nodes U1 and U3 works as a chemical index that will allow

us to differentiate galaxies A and B from galaxy C, even when they belong to the same population. Finally, galaxies that are in the tree canopy are the galaxies whose chemical composition are most similar, and, therefore, they have the longest distance to the root. Galaxies at the top of the tree end up being actually chemically different from galaxies at the root of the tree, even when they belong to the same population. Therefore the length between the nodes (Hereafter: NodeLength) along the tree, will help us to understand which parameters can influence the differentiation of galaxies from the top of the tree until the root.

In order to obtain a consistent result for our different galaxy samples, we will calculate 1,000 trees utilizing Montecarlo sampling from a normal distribution where the center of the distribution is the value of the absorption index and the width, the error of the measurement from SDSS DR14 (Abolfathi et al. 2018). Also, we make bootstrapping with replacement so that every time we calculate our distance matrix with Montecarlo sampling we will have a different combination of 29 or 30 absorption indices to generate our tree. Finally, we make a majority rule consensus, that considers structures in the tree that repeat at least a 50 % of the time in the trees that we calculated. This procedure allows us to eliminate branches that are not statistically significant.

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5.

Analysis

5.1.

Proof of concept

5.1.1.

Globular Cluster NGC2808

As a proof of concept, we calculate a phylogenetic tree for our sample of 117 stars in the globular cluster NGC2808. We obtain one main branch from the majority consensus tree of 1000 trees appearing730 times, as we can see in Fig 5.1.

The stars of the globular cluster where separated in to five groups in Carretta 2015 (Hereafter: C15) in order to define five populations as we can see in Fig 5.2 with the classical Na-Mg anticorrelation. They order the populations by the decreasing of Mg abundance, classifying them in to primordial or almost primordial abundance ratios (P1 and P2), intermediate composition (I1 and I2) and with severely extreme changes from the original composition (E). To be able to determine if two sets of data where significantly different from each other, they apply a Student’s and Welch’s test. They test the null hypothesis that any pair of components are extracted from a distribution having the same mean[element/F e], for[F e/H],[O/F e],[N a/F e],[M g/F e], [Al/F e],[Si/F e], and

[N a/M g]. They list the number of degrees of freedom, the t-value and the two-tailed

probability, finding that only E population seems to be statistically different from the intermediate and primordial populations.

We plot the Na-Mg anticorrelation highlighting the stars belonging to our main branch in Fig 5.3. We can notice that the stars of our main branch correspond to the E population define by C15. Therefore our phylogenetic analysis can be use to detect a population of stars chemically different from the original composition of the globular cluster.

In order to study which classes of indices influence our population with different composition, we re-calculate our consensus tree without a specific chemical element. We observe that if we remove [O/F e]I, [N a/F e]I, or [M g/F e]I, we get a tree with no structures. Therefore this three chemical elements are fundamental in the extreme population found.

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22 5.1 Proof of concept 37998_ID 39060_ID 32398_ID 41050_ID 32469_ID 50910_ID 44984_ID 46908_ID 56710_ID 4949 3_ID 40983_ ID 100 12_ID 491 22_ID 4760 6_ID 4609 9_ID 4324 7_ID 48 60 9_ID 51 93 0_ID 30 52 3_ ID 33 45 2_ ID 42 88 6_ ID 73 15 _ID 48 00 1_ ID 53 39 0_ ID 54 64 4_ ID 41 96 9_ ID 52 04 8_ ID 33 91 8_ ID 48 42 4_ ID 9 72 4 _ ID 13 575

_

ID

718 3_ ID

873 9_ID

13 983

_ID

326 85_

ID 5145 4_ID 4742 1_ID 4168 8_ID 4692 4_ID 5151 9_ID 5426 4_ID 4686 8_ID 4120 7_ID 3787 2_ID 3076 3_ID 8826 _ID 4452 6_ID 4801 1_ID 5011 9_ID 46520_

ID 31851_

ID 55822_

ID 31361_ID 47502_ID 46587_ID 46663_ID 41008_ID 51918_ID 10341_ID 52006_ID34008_ID 49743_ID53284_ID

38967_ID10571_ID 4549650761_ID_ID

10204321_ID17_ID 542 84_ID 506 85_ID 478 05_ID 4642 2_ID 45 701_ ID 5320 9_ID 37 49 6_ID 45 44 3_ ID 54 75 6_ID 82 04 _ID 37 50 5_ ID 56 92 4_ ID 41 82 8_ ID 10 26 5_ ID 75 58 _ ID 34 63 4_ ID 43 09 7_ ID 35 26 5 _ ID 3 82 4 4 _ ID 4 8 8 8 9 _ ID 5 56 09_ ID

309 00 _ID

519 83_

ID

44 996

_ID

446 65_

ID 3292 4_ID 5125 6_ID 4975 3_ID 5535 4_ID 5362 9_ID 3182 3_ID 7536 _ID 5289 1_ID 5603 2_ID 4658 0_ID 3290 9_ID 3866 0_ID 3072 0_ID 3783 1_ID

38228_ ID 8603_I D 42996_ ID 42122_ ID 51499_ID 10105_ID 46036_ID 43794_ID 52647_ID 0.0154287

Figura 5.1: Consensus phylogenetic tree of the globular cluster NGC2808. The red shaded area highlight the main branch of the phylogenetic tree. The numbers correspond to the ID of each star in the globular cluster.

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Figura 5.2: Mg and Na anticorrelation from figure 8 C15. Different colours indicate different groups, blue (P1), green (P2), red (I1), orange (I2), and black (E)

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24 5.1 Proof of concept

0 0:5

[Na/Fe] 0

0:2 0:4

[M

g

/

F

e]

Figura 5.3: Na-Mg anticorrelation of the globular cluster NGC2808, with the five groups define by C15 differentiated by color. Blue (P1), green (P2), red (I1), orange (I2), and black (E). The magenta hollow squares represent the stars in our main branch of the phylogenetic tree.

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Population No. of members

Branch 1 10

Branch 2 18

Branch 3 67

Branch with 1 node 90

Branch with 2 node 39

Branch with 3 node 18

Branch without nodes 233

5.2.

Phylogenetic study in Galaxies

5.2.1.

The Coma Cluster

We calculate a phylogenetic tree for our galaxy sample of the Coma cluster. Our tree presents three main branches that we arbitrarily named branch one (B1), branch two (B2) and branch three (B3). From the majority consensus rule of 1,000 trees, they appear in 683, 694 and 655 trees, respectively. Several other minor branches are found that appear at least 50% of the time and whose complete description is shown in table 5.1.

Each of our branches represents a GP and they are differentiated by their chemical content. In what follows, we will focus in the three main GPs B1, B2 and B3. In order to prove that our GPs are different, we plot them in Color-Magnitude space, indicating also galaxy morphology.

From Figure 5.4, branches B1 and B2 belong to the bright-end of Red Sequence, and B3 belongs to the blue cloud of the cluster. This shows us that at least populations B1 and B2 are different from population B3, because they belong to different areas in the Color-Magnitude diagram. From the consensus morphology, we see that B1 has 3 elliptical galaxies and 7 S0 galaxies, B2 has 15 elliptical galaxies and 3 S0 galaxies, whereas B3 has 50 spiral galaxies and 17 S0 galaxies. We plot each population as a single tree so the morphology can be visualized. (See 5.5, 5.6 and 5.7).

If we look at how these GPs are distributed in a sky projection in the galaxy cluster cluster, from figure 5.8 we see that that 1) galaxies in B1 population show lenticular morphology at the outskirts of the cluster and elliptical morphology in the cluster core; 2)

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26 5.2 Phylogenetic study in Galaxies

12 13

14 15

16 17

r 1:0

1:5

B

¡

r

Spiral Elliptical S0

CCG B1 B2 B3

Figura 5.4: Color-Magnitude diagram of the Coma Cluster with photometric filters Johnson B and Sloan r. Triangles, circles and squares represent galaxies belonging to branch 1 (B1), branch 2 (B2) and branch 3 (B3), respectively. The colors indicate galaxy morphology where red corresponds to elliptical galaxies, blue to spiral galaxies, and yellow to S0 galaxies.

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0.125

587739

706328

350792

0.547 0.0651

58 77

41 72

17 49

74 99 06

1.17 0.243

5877

4172

2823

6226

94

0.437

0.12 0.127

587741

603109

666819

0.529 0.0772

0.0333

587741722823688327 0.557

587 741

603109

732 429 0.479

0.248

58 77

41 60 14

98 79 19

58

0.8

73 58

7741

7233

6101

7971

0.5

587741

602035

400774

0.439

587741722823819408

0.472

Force topology is enabled! Branch lengths do not represent real values.

587741723361017971

587741722823622694

587741602035400774

587741722823819408

587739706328350792

587741721749749906

587741601498791958

587741603109732429

58774172282368827

587741603109666819

0.12

0.08

0.24

0.12

0.12

0.07

0.03

Figura 5.5: Branch B1 of the phylogenetic tree of the Coma Cluster that represents our first galaxy population. Each galaxy has its ID number from the SDSS DR7, and its image from the SkyServer DR15. The number between the nodes is the length of their separation.

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28 5.2 Phylogenetic study in Galaxies 0.0673 0.13 5 587741603109863548 0.729 0.247 0.13 8 0.07 73 0.112 58774172 22866863 27 0.459 5877 4160 2035 5973 17 0.5 03 0.0671 58 77 41 60 25 72 59 93 52 0.488 0.171 0.123 5 8 7 7 4 1 6 0 3 1 0 9 6 0 1 3 2 1 0.667

587 741

722 823

81 927

1 0.714 5877 4160 2573 0580 54 0.309 5877 4160 3109 7979 94 0.655 58773971 92169881 84 0.528 587741722286620734 0.593 0.153 5877 41722286

489633 0.498

5877 4172 2823 8849 62 0.288 58 77 41 72 22 86 62 06 77 0.337 5 8 7 7 4 1 7 2 2 8 2 3 9 5 0 3 8 8 0.49 5 87 741

603 109

535 846

0.301 5877 4172 2286 6862 55 0.553 5877 4160 2572 4682 85 0.475 58774172 28237538 11 0.719

Force topology is enabled! Branch lengths do not represent real values.

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

x

587741602035597317

587741603109601321

587741602573058054

587741722286686255

587741603109535846

587741722823950388

587741722286620677

587741722823884962

587741722286489633

587741722286620734

587741722823819271

587741603109863548

587741602572468285

58774172282375381

1

587741722286686327

587741602572599352

587739719216988184

0.06

0.15

0.13

0.24

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0.07

0.1

1

0.06

0.17

0.12

587741603109797994

Figura 5.6: Branch B2 of the phylogenetic tree of the Coma Cluster that represents our second galaxy population. Each galaxy has its ID number from the SDSS DR7, and its image from the SkyServer DR15. The number between the nodes is the chemical length of their separation.

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1 0.148 587 741 722 286 751 847 1.09 58 77 41 60 31 09 33 92 67 1.27 10.236 1 0.291 58 77 41 72 17 49 94 65 64 2.97 1 0.279 1 0.386 58 77 41 60 25 72 92 70 50 1.5 58 77 41 60 31 09 79 80 90 1.73 58 77 41 60 20 35 85 94 78 1.91 587 741 722 286 751 864 3.82 587 741 602 035 794 045 1.91 58 77 41 72 12 13 01 00 62 1.72 58 77 39 71 92 17 31 60 96 3.12 1 0.448 58 77 41 72 33 60 95 24 88 1.18 1 0.346 58 77 39 71 92 16 98 82 93 1.61 58 77 41 60 14 98 98 86 19 1.65 1 0.352 58 77 41 60 25 72 59 94 54 2.95 58 77 39 71 92 17 64 35 95 1.58 58 77 41 60 25 72 59 94 34 2 1 1.38 58 77 39 70 63 28 48 19 15 2.15 5 8 7

741601498

988667

10.3 5 8 77 4 1 7 2 2 2 8 7 2 7 6 1 1 5 2.85 1 0.234 1 0.444 5 8 7 7 4 1 6 0 2 5 7 2 5 9 9 3 0 8 0.344 58 7 7 4 1 7 2 2 2 8 6 7 5 18 1 2 0.901 58 77 41 60 25 72 53 38 92 1.42 58 77 41 60 31 09 40 47 87 3.64 58 77 41 60 31 09 60 13 23 1.08 58 77 41 72 22 86 75 19 67 1.59 58 77 41 60 14 99 11 97 66 0.877 1 0.4 1 0.394 58 77 39 71 92 17 11 93 07 0.483 58 77 41 72 28 23 95 04 91 0.973 1 0.105 1 0.17 1 0.241 587 741 722 823 819 344 0.832 10.353 587 741 602 572 926 978 0.625 587 741 722 286 751 749 1.01 739 587

719 754 514 434 0.875 587 739 706 328 481 876 0.964 587 741 602 035 859 486 0.748 58 77 41 60 20 35 85 95 37 0.75 1 0.219 10.523 1 0.47 58 77 41 60 25 72 79 61 10 2.53 1 0.21 58 77 41 72 22 86 94 85 19 1.63 58 77 41 60 25 72 73 05 42 2.41 58 77 41 72 33 60 55 92 52 1.71 587 741 602 572 795 949 1.23 10.158 587 741 722 823 819 456 1.14 58 77 41 72 28 23 62 28 33 1.21 1 0.235 58 77 41 60 25 72 46 82 65 1.02 58 77 41 72 22 86 94 85 49 1.54 10.151 58 77 41 60 31 09 47 02 60 1.99 58 77 41 72 22 87 34 16 19 1.16 58 77 41 60 31 09 40 47 12 2.31 58 77 41 60 31 09 53 59 24 0.927 58 77 41 72 28 23 88 50 80 1.67 58 77 41 72 22 86 29 31 55 1.5 58 77 39 70 63 28 21 97 69 1.07

58774160203559746

3 3.08 5 8 7 7 4 1 60 3 1 0 9 7 3 2 5 5 5 2.59 5 8 77 4 1 6 0 1 4 9 9 0 5 4 2 3 8 1.31 58 77 41 72 28 23 42 62 25 0.863 1 0.232 58 77 41 60 25 72 73 03 95 0.687 58 77 41 72 28 23 81 93 45 1.1 58 77 41 60 31 09 92 90 77 1.29 58 77 41 72 28 23 68 85 06 1.18 58 77 39 71 92 17 51 25 39 2.08 58 77 41 72 28 23 55 71 34 0.964 58 77 41 60 25 72 53 39 09 2.19 1 0.0866 587 741 602 035 663 009 1.01 1 0.254 587 741 602 035 466 319 0.933 1 0.128 587 741 722 286 424 180 1.08 587 741 602 573 254 708 1.06 587 741 722 286 882 926 0.971

Force topology is enabled! Branch lengths do not represent real values.

587741603109798090 587741602572927050 587741721749946564 587741603109339267 587741722296751847 587741722286882926 587741602573254708 587741722286424180 587741602572533892 587741602035466319 587741602035663009 587741602572533909 587741722823557134 587739719217512539 587741722823688506 587741603109929077

587741722823819345587741602572730395587741722823426225587741601499054238 587741603109732555 587741602035597463 5877439706328219769

5877416014991 19766 587741722286751967 587741603109404787 587741722286751812 587741602035859478 587741722286751864 587741602035794045 587741721213010062 587739719217316096 587741723360952488 587739719216988293 587741601498988619587741602572599454

587739719217643595 587741602572599434 587741601498988667 5877417222872761

15 587741602572599308 587739706328481915 587741603109601323 5877416020358559486 587739706328481876 587739719754514434 587741722286751749 587741602572926978 587741722823819344 587741722823950491 5877397192171 19307 5877416020358559537 587741602572796110 587741602572730542 587741723360559252 587741602572795949 587741722823885080 587741603109535924 587741603109470260587741722286948549 587741602572468265587741722823622833 587741722823819456 587741722286293155 587741603109404712 587741722286948519 587741722287341619

Figura 5.7: Branch B3 of the phylogenetic tree of the Coma Cluster that represents our third galaxy population. Each galaxy has its ID number from the SDSS DR7, and its image from the SkyServer DR15. The number between the nodes is the length of their separation.

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30 5.2 Phylogenetic study in Galaxies

galaxies in B2 population are distributed in two clumps in the cluster, one in the center and the other near the galaxy NCG 4839 which is associated with a subgroup of galaxies in-falling into Coma Cluster (Neumann et al. 2001); and 3) galaxies in B3 population do not show any preferential distribution in the cluster.

In order to characterize the common properties of the GP, we compare their stellar massES, sSFRS, metallicities and ages in Figure 5.9. From this comparison we can conclude that B1, B2 and B3 are indeed three different GPs. B1 galaxies are quiescent with a high stellar mass (log(M/M) = 10,35−11,17), high metallicity ([Z/H] = 0,24−0,59), low sSFR

(10−11,2510−10,53 yr−1), however of predominantly S0 morphology and with

young-to-intermediate age stellar populations (1,88−5,38 Gyr). On the other hand, B2 galaxies correspond to quiescent galaxies with high stellar mass (log(M/M) = 10,62−11,76), high

metallicity ([Z/H] = 0,21−0,49), low sSFR (10−11,25−10−10,53 yr−1),

intermediate-to-old-age stellar populations (<3,74Gyr) and mostly of elliptical morphology. B3 galaxies have low stellar mass (log(M/M) = 8,39−10,41) with low metallicity ([Z/H] =−1,65−0,55)

and high sSFR (10−10,2510−8,17 yr−1), of predominantly spiral morphology and with

stellar populations of a wide range in age (0,12−10,89 Gyr).

Now we analyze each branch’s hierarchical structure. As we show in section 4.1, the NodeLength works as a chemical index . This chemical index indicates the variation in the chemical composition of galaxies. In order to see how the general properties of mass, sSFR, ages and[Z/H] relate internally in our GP, we add the node length from the root of the tree to the leaves where each galaxy is. See fig. 5.10

We calculate the Pearson and Spearman correlation coefficients between the NodeLength and the stellar mass, metallicity, ages, and sSFR to see which of these properties is the main driver of the measured chemical gradient by determining if any linear or monotonic correlation exists. The results are summarized in table 5.2. We can see that B1 anti-correlates with age and sSFR, while it anti-correlates with metallicity. Also, B3 presents a monotonic correlation with sSFR. This even shows us when our GP have different stellar mass ranges, although stellar mass is not relevant in their hierarchical relationships. StellaR mass and sSFR do not play any role in the hierarchical structure of our phylogenetic tree either.

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12h55m00

13h00m00

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±

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±

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o

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t

=

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eg

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Figura 5.8: Projected sky distribution of galaxies in the Coma Cluster belonging to different branches of the phylogenetic tree. Triangles, circles and squares represent galaxies belonging to branch 1 (B1), branch 2 (B2) and branch 3 (B3), respectively. The colors indicate the morphology of the galaxy where red corresponds to elliptical galaxies, black to spiral galaxies, and magenta to S0 galaxies. The color scale shows the number count of galaxies by degree squared in the sky for Coma cluster. White star points the galaxy NGC4839.

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32 5.2 Phylogenetic study in Galaxies

A)

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Figura 5.9: The histograms A, B, C and D show the distribution of galaxies from the three different branches B1, B2 and B3 with respect to stellar mass, metallicity, age and sSFR. The yellow, red and blue colors represent galaxies from branches B1, B2 and B3, respectively.

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B1

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2

Log(NodeLength)

9

10

11

L

o

g

(M

a

ss

)

0:1 0:2

0:5

1

2

Log(NodeLength)

¡11

¡10

¡9

L

og

(S

S

F

R

)

Figura 5.10: Panels A, B, C and D, show a comparison of our chemical index (length between nodes) with stellar mass, metalicity, age of the stellar population, and sSFR, respectively. Triangles, circles and squares represent B1, B2 and B3 GP. The red, yellow and blue colors represent elliptical, lenticular and spiral morphology, respectively.

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34 5.2 Phylogenetic study in Galaxies

Cuadro 5.2: Pearson and Spearman coefficients between NodeLength and common properties of galaxies for each galaxy population

Branch Pearson coefficient Spearman coefficient

Length v/s Mass

B1 0.12 -0.092

B2 0.351 0.436

B3 -0.303 -0.362

Length v/s [Z/H]

B1 0.681 0.771

B2 0.388 0.444

B3 -0.250 -0.316

Length v/s Age

B1 -0.861 -0.856

B2 0.439 0.332

B3 0.443 0.462

Length v/s SSFR

B1 -0.536 -0.355

B2 0.129 0.115

B3 0.490 0.599

differences or common characteristics of galaxies in our GP are that determine the hierarchical structures we observe. Therefore we separate our abundance indices in five classes: (1) absorption Balmer lines withHδA,HδF,HγA,HγF,Hβ andHβG; (2) positive response to α/F eenhancement withCN1, CN2,M g1,M g2,M gb, Ca4227and G4300; (3)

negative response to α/F e enhancement with F e4383, F e4531, F e4930, F e5015,F e5270,

F e5270S,F e5335,F e5406 andF e5709; (4) Emission Line[OIII]α5007, with[OIII1]and

[OIII2] (Gonzalez et al. 2005); and (5) insensitive to α/F e withN aD, C4668, F e5782,

Ca4455, T iO1 andT iO2. Then we recalculate the phylogenetic tree with the same sample

of galaxies but without one of these classes. We analyze our re-calculated consensus tree, by plotting color-magnitude diagrams. We graph the distribution of galaxies from our original tree, and that of the galaxies that appears in our re-calculated trees (see figure 5.11). We resume this results in Table 5.3. Now that we can see which classes of indices influence our GP, we can study in more detail the internal structure of our GP, analyzing the relations between each index and the NodeLength. (see figure 5.12, 5.13, 5.14). If an absorption index have a high correlation with NodeLength and at the same time have different range of values for each galaxy populations, this index is responsible for the

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Our main findings are:

•Absorption Balmer lines: from table 5.3 we can see that only the B2 population remains

in our tree. Balmer lines decrease in strength as stellar populations get older, which is reflected in their influence on populations B1 and B3 (See figure 5.13-D). From plots D.1 to D.6 in figure 5.14 we see that Balmer lines have a high correlation for each galaxy population, however HδA (see figure 5.13-D.1) is the index that has a different value for each galaxy population. This analysis shows us that the HδA index is important for breaking the degeneracy between age and horizontal branch morphology Schiavon et al. 2004.

• Insensitive to α/F e enhancement: this abundance indices are relevant for the B1

population, because as we see in table 5.3 and figure 5.13-B that B1 population is not present in our recalculated tree. Analyzing individual abundance indices, NaD index (see figure 5.13-B.1)) show a strong correlation with a different value for each GP. This absorption index measures Carbon, Magnesium and Sodium, elements that are produced and released to the interstellar medium by massive stars. This tells us that galaxies in B1 have undergone a period of star formation, and this is the reason for showing up in our phylogenetic tree as a separated galaxy population.

• Negative Response to α/F e enhancement: at first glance from table 5.3, we see that

the re-calculated tree, has tree main GP. But if we look at figure 5.10-A, we can notice that the B3 population is missing its S0 galaxies closer to the red sequence. TheF e4383 abundance index (see figure 5.12-A.1), show a correlation and different values for this S0 with other populations. These index measure Carbon, Iron and Magnesium, elements that are produced in Type Ia supernovae, indicating that there is a difference between S0 galaxies from population B1 and B3.

• Positive Response to α/F e enhancement: From figure C) 5.13 we see that the presence

of these lines are not relevant for the identification or hierarchical structures of our GP, because we obtain the same galaxy populations without this absorption indices.

• Emission Line [OIII]α5007, with [OIII1] and [OIII2] (Gonzalez et al. 2005): the

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36 5.2 Phylogenetic study in Galaxies

Cuadro 5.3: Remaining galaxy populations for Recalculated phylogenetic trees without a specific set of line indices

Index Class Branches

Blamer Lines B2

Positive response to alpha/Fe enhancement B3 B2 B1

Negative response to alpha/Fe enhancement BE B3 B1

Insensitive to alpha/Fe B3 B2

Emission Line $[OIII] \alpha 5007$ B2 B3

population. This indices not present correlations, have similar values for all our GPs (See figure 5.14). Therefore this indices are irrelevant for finding galaxy populations and their internal structure.

From this analysis we can infer that the minimum amount of indices that we need to perform a successful and consistent phylogenetic study is 18 (see figure 5.12, 5.13. 5.14), and those include the following ones:HδA,HγA ,HγF,Hβ,HβG,CN1, CN2,M g1,M g2,

M gb,G4300,N aD,C4668,T iO2,F e4383,F e5270,F e5270S,F e5335. We investigated the

possibility of carrying such analysis with fewer indices. The results showed inconsistencies in the sense that the MC trials with bootstrapping delivered different outcomes in terms of tree structures. Hence, we do not recommend to apply such phylogenetic method with indices other than those indicated above.

5.2.2.

The Field

One of the main drivers of galaxy evolution is the environment (Kauffmann et al. 2003, Kauffmann et al. 2003, Baldry et al. 2006, Peng et al. 2010). Therefore, in order to assess the differential effect between high and low density environments, we generated a phylogenetic tree with 438 field galaxies homogeneously distributed in the sky (see figure 5.15), at the coeval redshift range of Coma 0,034−0,054. From our consensus tree, we obtain a main branch with 46 galaxies that appears 561 times from 1,000 tree samples, and several minor structures (220 branches with 1, 2, 3, or four nodes and 172 in branches without nodes). We interpret the main branch as our main GP.

This population presents galaxies predominantly of lenticular morphology, that we can observe in more detail in figure 5.16, with high stellar masses (log(M/M) = 10,01−11,32)

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B1

12 14

16

r 1:0

1:5

B

¡

r

12 13 14 15 16

17

r 1:0

1:5

B

¡

r

12 13 14 15 16

17

r 1:0

1:5

B

¡

r

12 13 14 15 16

17

r 1:0

1:5

B

¡

r

12 14

16

r 1:0

1:5

B

¡

r

B2

B3

Galaxies

Elliptical

S0 Spiral

A) B)

C) D)

E)

Figura 5.11: Color-magnitude diagram of our Coma cluster galaxy sample with photometric filters Johnson B and Sloan r. Panels A, B, C, D, and E show a recalculated phylogenetic tree without, negative response to α/F e enhancement, insensitive response

to α/F e enhancement, positive response to α/F eenhancement, absorption Balmer lines,

and absorption line indices[OIII], respectively. The cyan diamonds represent the galaxies that appear in the branches of each recalculated tree.

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38 5.2 Phylogenetic study in Galaxies

0:1 0:2 0:5 1 2 Log(NodeLength) ¡8 ¡6 ¡4 ¡2 0 2 4 6 8 F e4 3 8 3 A.1)

0:1 0:2 0:5 1 2

Log(NodeLength) ¡8 ¡6 ¡4 ¡2 0 2 4 6 8 F e4 5 3 1 A.2)

0:1 0:2 0:5 1 2

Log(NodeLength) ¡2 ¡1 0 1 2 3 F e4 9 3 0 A.3)

B1 SC:0.512 B1 SC:-0.435 B1 SC:0.559

B2 SC:0.070 B2 SC:0.092 B2 SC:0.282

B3 SC:-0.652 B3 SC:-0.510 B3 SC:-0.615

0:1 0:2 0:5 1 2

Log(NodeLength) ¡6 ¡4 ¡2 0 2 4 6 8 F e5 01 5 A.4) B1 SC:0.229 B2 SC:0.264 B3 SC:-0.824

0:1 0:2 0:5 1 2 Log(NodeLength) 0 1 2 3 F e5 2 7 0 A.5)

0:1 0:2 0:5 1 2 Log(NodeLength) 0 1 2 F e5 2 7 0 S A.6) B1 SC:0.326 B2 SC:0.178 B3 SC:-0.675 B1 SC:0.057 B2 SC:0.244 B3 SC:-0.738

0:1 0:2 0:5 1 2 Log(NodeLength) 0 1 2 3 F e5 3 3 5 A.7)

0:1 0:2 0:5 1 2

Log(NodeLength) ¡1 0 1 2 F e5 4 0 6 A.8)

B1 SC:0.625 B1 SC:0.377

B2 SC:0.419 B2 SC:0.108

B3 SC:-0.817 B3 SC:-0.671

0:1 0:2 0:5 1 2

Log(NodeLength)

¡0:5 0

0:5

1:0

1:5

F e5 70 9 A.9) B1 SC:-0.221 B2 SC:-0.026 B3 SC:-0.340

0:1 0:2 0:5 1 2

Log(NodeLength) 0 1 2 3 4 5 N a D

0:1 0:2 0:5 1 2

Log(NodeLength) ¡2 0 2 4 6 8 C 4 6 6 8 B.1) B.2) B1 SC:0.252 B1 SC:0.800 B2 SC:0.578 B2 SC:0.839 B3 SC:-0.533 B3 SC:-0.408

0:1 0:2 0:5 1 2

Log(NodeLength) ¡2 ¡1 0 1 2 F e5 7 8 2 B.3) B1 SC:0.476 B2 SC:-0.041 B3 SC:-0.118 Spiral Elliptical S0 B1 B2 B3

A.1 - A.9) Negative Response to alpha/Fe enhancement B.1 - B.6) Insensitive to alpha/Fe

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